What's the best way to determine, through JDBC, if a table exists in the database?

One way is to run a query on that table and catch the exception. (E.g. "SELECT count(*) from table_name"). If no exception is thrown, table exists, otherwise not.

There has got to be a better way than this. Does standard SQL provide any such mechanism? A quick search didn't reveal anything.

Not to mention, DB independent mechanism would be preferred.

Definitely do not use:
SELECT count(*) from table_name

That will take too long if the table has lots of rows. You could try:
SELECT 1 from table_name

You could also query the SYSCAT.TABLES catalog view, which has a list of all the tables in the database. Besure to check on TYPE because not everything in there is actually a base table (some are views, etc.).

I don't believe there would be a DBMS-independent way of doing this. Even if you attempt to analyze an exception thrown during the query, it will still be database-dependent. That is, it will of course be a SQLException; however, you'll need to analyze the returned error code to make sure it's thrown because of a missing table definition and not because of some communication problem or insufficient privileges...

JDBC provides a standard interface to the database catalog, Connection.getMetaData(), while the driver takes care of the DBMS specifics. Have a look at the DatabaseMetaData.getTables() definition in the JDBC API.

That's a good one... Very close to being vendor-independent, although the "catalog" and possibly "schema Pattern" might change. According to the docs, you can throw nulls into those, which makes it reasonably vendor-independent.